temporal coherence and spectral linewidth of an injection ...temporal coherence and spectral...

Temporal coherence and spectral linewidth of an

injection-seeded transient collisional soft x-ray

laser

L. M. Meng,1,* D. Alessi,

2 O. Guilbaud,

3 Y. Wang,

2 M. Berrill,

2 B.M. Luther,

2 S. R.

Domingue,2 D. H. Martz,

2 D. Joyeux,

4 S. De Rossi,

4 J. J. Rocca,

2 and A. Klisnick

1

1ISMO, Bât. 350, CNRS, Université Paris-Sud 11, 91405 Orsay, France 2NSF Center for EUV Science and Technology, Colorado State University, Fort Collins, CO, USA

3LPGP, Bât. 210, CNRS, Université Paris-Sud 11, 91405 Orsay, France 4LCFIO, Institut d’Optique-Graduate School, 91128 Palaiseau, France

*[email protected]

Abstract: The temporal coherence of an injection-seeded transient 18.9 nm

molybdenum soft x-ray laser was measured using a wavefront division

interferometer and compared to model simulations. The seeded laser is

found to have a coherence time similar to that of the unseeded amplifier,

~1ps, but a significantly larger degree of temporal coherence. The measured

coherence time for the unseeded amplifier is only a small fraction of the

pulsewidth, while in the case of the seeded laser it approaches full temporal

coherence. The measurements confirm that the bandwidth of the solid target

amplifiers is significantly wider than that of soft x-ray lasers that use

gaseous targets, an advantage for the development of sub-picosecond soft x-

ray lasers.

©2011 Optical Society of America

OCIS codes: (140.7240) UV, XUV, and X-ray lasers; (300.6300) Spectroscopy, fourier

transforms; (300.6560) Spectroscopy, x-ray.

References and links

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#145253 - $15.00 USD Received 15 Apr 2011; revised 25 May 2011; accepted 25 May 2011; published 7 Jun 2011(C) 2011 OSA 20 June 2011 / Vol. 19, No. 13 / OPTICS EXPRESS 12087

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x-ray lasers,” Opt. Lett. 31(20), 3043–3045 (2006).

The demonstration of injection-seeded soft X-ray lasers (SXRL), generated by either transient

collisional excitation in solid target plasmas [1] or optical-field-ionization in gaseous targets

[2], has opened new prospects for the utilization of high-brightness plasma-based coherent

soft x-ray sources for various applications. The use of high-order harmonic (HH) pulses as a

seed has led to a dramatic enhancement of the spatial coherence [3,4] over those exhibited in

amplified spontaneous emission (ASE) operation. The degree of temporal coherence is an

important parameter that also needs to be characterized for applications. The coherence time,

linked to the spectral width ∆ν of the laser line through τc ~1/∆ν, also determines the ultimate

minimum pulse duration that can be achieved. The shortest pulse duration measured to date

for a seeded SXRL is ~1.1 ps in a Ne-like Ti plasma [5]. In order to make further progress

towards sub-picosecond pulse soft x-ray lasers [5,6] it is important to obtain experimental

information about the spectral characteristics of these sources. This is a challenging

measurement because the narrow linewidth of SXRL lines (typically ∆λ/λ ~105

) typically lies

beyond the resolution limit of existing spectrometers in this spectral range.

In this paper we report the first measurement of the temporal coherence and spectral width

of a transient solid-target SXRL injection-seeded by HH pulses. Measurements for a seeded

18.9 nm Ni-like Mo amplifier were compared to results for the ASE mode of operation and

model simulations. It is shown that the injection-seeded and ASE lasers have a similar

linewidth, but that the degree of temporal coherence of the seeded laser is significantly larger,

approaching full temporal coherence. The narrow linewidth was resolved using a wavefront-

division interferometer specifically designed to measure temporal coherence [7] from which

the spectral linewidth is inferred. Such interferometer was previously used to investigate other

types of SXRLs, including a 32.8 nm injection-seeded optical-field-ionization (OFI) SXRL in

a Xe gas medium developed at Laboratoire d’Optique Appliquée (France) [8,9]. The transient

amplifiers created by irradiation of solid targets [10] studied here are measured to have

significantly larger linewidths that support the generation of shorter pulse durations.


Fig. 1. (a) Experimental set up used to measure the temporal coherence of an 18.9 nm

molybdenum plasma amplifier. Interferograms of the ASE (b) and seeded (c) 18.9 nm laser beam with a zero path difference between the arms of the interferometer. A 300 nm thick

aluminum filter was used. In the ASE case (b) the beam is composed of several juxtaposed

speckle structures. Two of them are apparent (orange white zones) in the fringe area. In the

seeded case (c) one single spot is apparent, corresponding to the amplified seed beam.

The experiment was carried out at Colorado State University (CSU) using a 18.9 nm

SXRL amplifier in the transient regime generated by irradiation of a solid molybdenum slab

target at grazing incidence [11, 12] with pulses from an λ = 800 nm Titanium:Sapphire

(Ti:Sa) laser. A sequence of two 210 ps FWHM duration pulses with energies of 45 mJ and

420 mJ are focused onto a 30 µm wide by 4 mm long line at normal incidence to the target

producing a plasma with a large fraction of the ions in the Ni-like state. At a delay of 500 ps,

a 3.3 ps FWHM duration heating pulse of 1J energy impinges onto the plasma at a grazing

incidence angle of 23 degrees in an overlapping line focus, resulting in transient population

inversion at 18.9nm. This laser amplifier was seeded with the 43rd harmonic of a

femtosecond pulse from a Ti:Sa laser as described in [3] yielding a highly collimated, almost

fully spatially coherent beam. The duration of the Ti:Sa pulses used to generate the high

harmonic seed in this experiment was ~100fs. The output characteristics of the seeded laser

are similar to that described in [3]. The SXRL beam was directed toward a variable path-

difference interferometer which was set at a distance of 3 m from the source (Fig. 1(a)). A far-

field monitor, consisting of a 45 degrees multilayer mirror and an XUV CCD camera could be

inserted in the X-ray laser beamline (see Fig. 1(a)) to allow verification of the beam alignment

before each series of measurements. The interferometer consists of a pair of dihedrons slightly

tilted towards each other and irradiated under 6 degrees grazing incidence [7]. Interference

fringes, which are formed in the overlapping region, are detected with a XUV CCD camera.

The CCD chip is inclined to a 35 degrees incidence angle in order to increase the apparent

fringe spacing to ~5 pixels/fringe. A variable path difference between the two interfering


beamlets is introduced by translating one of the two dihedrons vertically. Using a dihedron

instead of a flat mirror ensures that the loss of fringe visibility when the path difference is

increased is solely due to the finite temporal coherence, not to a geometrical change in the

beam overlap, which depends also of the finite spatial coherence of the source. The tilt angle

between the interfering mirrors is 1.6 mrad, leading to an interference field of 1 mm in the

plane normal to the beam, or 1.8 mm in the CCD detector plane.

Fig. 2. (a) Visibility as a function of the path difference measured in the injection-seeded mode for the plasma amplifier lengths of 2 mm (a), 3 mm (b) and 4 mm (c). (d) Visibility data

corresponding to the 4 mm ASE amplifier. The solid-line curves show the best analytical fit of the experimental data. Different types of analytical functions were used: (a) sum of two

Gaussians; (b) sum of Gaussian and decreasing exponential; (c) decreasing exponential; (d)

sum of two Gaussians

Series of interferograms with increasing path difference were acquired for different X-ray

laser amplifier lengths. Figure 1 (b, c) shows two typical interferograms of the 18.9 nm laser

obtained in the ASE mode and injection seeded mode respectively. In the ASE case, the beam

is composed of randomly distributed speckles [13] which are apparent in the image. In the

injection seeded case, the highly-collimated amplified HH beamlet is centered on the

interference region [10]. Each interferogram was processed numerically to infer the fringe

visibility for a given path difference. After background subtraction, a Fourier-transform with

a sliding window [8] was applied to the full interference zone, yielding a map of visibility.

The visibility was found to vary by about 20% across the zone of interest in the ASE case.

This variation can be attributed to the non-uniformity of the X-ray laser beam [14] which can

be seen in the images shown in Fig. 1. When the two non-uniform beamlets overlap, the

visibility of the fringes is maximum only at those positions where the intensities in the two

interferometer arms are equal and it is lower elsewhere. Hence the maximum visibility in the

interference field was considered as the relevant value for a given interferogram. For the

injection seeded case, the visibility was measured in a restricted zone containing the amplified


HH beamlet, excluding the ASE zone. In this restricted zone the variation of visibility is

smaller than in the ASE case, namely less than 10%.

Figure 2 (a-c) shows the measured visibility curves obtained from the path difference

scans for three different injection seeded Mo amplifier lengths. Figure 2(d) shows the

measured visibility curve corresponding to the 18.9 nm laser amplifier (L = 4 mm) operated

in the ASE mode. Each data point is the average of the visibility measured over 5 to 10 laser

shots, and the error bar represents the standard deviation, mainly due to shot-to-shot

fluctuation. In each graph, the solid-line curve shows the best analytical fit of the

experimental data. To infer the coherence time τC and the corresponding frequency linewidth

∆ν from our measurements we used the definitions given in [15], assuming that the spectral

profile is symmetrical with respect to the central frequency :

2 2 2 2

2 20 0

2 2

0 0

( ) ( )2

( ) ( )c

t V t dt G d

V t dt G d

(1)

where V(t) is the visibility as a function of the path difference (given by the analytical fit),

G(ν) is the spectral power density and is the average central frequency of the line. G(ν) is

given by the Fourier-transform of V(t). The above definitions, which are based on the

quadratic mean of the quantities, are less sensitive to the shape of the visibility curve (i.e. to

the chosen fit for the experimental data) than the usual definitions used previously [9, 14, 16].

Hence it can be judged as more appropriate in cases like ours where the shape of the visibility

curve is difficult to determine accurately.

0

1

2

3

4

5

6

0 1 2 3 4plasma length (mm)

∆n(1

011 H

z)

calculated seeded

calculated ASE

experiment seeded

experiment ASE

Fig. 3. Measured and computed linewidth (as defined in Eq. (1) of the injection-seeded and

ASE 18.9 nm molybdenum SXRLs for different plasma lengths (see color online).

The variation of the linewidth of the seeded and ASE lasers as a function of amplifier

length was simulated using the combination of a 2-dimensional hydrodynamic/atomic physics

code and a 3-dimensional ray propagation code developed at CSU. The ray propagation tracks

the amplification for each frequency component as the individual rays propagate taking into

account refraction and gain saturation [10]. While this code does not allow the full self-

consistent treatment of Maxwell-Bloch codes [17], it does include temporal broadening due to

bandwidth narrowing and has the advantage of including a more detailed atomic model. The

code was previously shown to satisfactorily predict the physical behavior as well as the pulse

duration and energy of injection-seeded transient soft x-ray lasers in agreement with

experiments [3,5]. The evolution of the plasma parameters was computed by the


hydrodynamic code and fed into the ray propagation code. The ray propagation calculation is

fully resolved in space, angle, frequency, and time. Figure 3 displays the values of the

measured and simulated quadratic linewidth of the injection-seeded and ASE lasers for

different plasma lengths obtained using the expression defined in (1). It can be observed that

smaller spectral linewidth (2.2 × 1011

Hz) corresponding to the larger temporal coherence

time, (1.0 ± 0.2) ps is obtained for the longest plasma length of 4 mm, as expected from

amplified radiation in the absence of saturation rebroadening. However, since most of the line

narrowing due to amplification occurs in the first 2 mm of the plasma column, the measured

variations as a function of plasma length are small and mostly within the error bars. It is also

observed that the linewidth of the ASE X-ray laser, 1.95 × 1011

Hz, is slightly smaller

(although again within the error bars) than the injection-seeded laser linewidth corresponding

to the same amplifier length, as already observed for the 32.8 nm OFI SXRL in a recent

experiment [9]. Such a behavior is consistent with the numerical simulations, and reflects the

fact that the linewidth of the ASE and seeded lasers are dominated by the bandwidth of the

amplifier, that is in turn dependent of the plasma conditions. There is no line rebroadening

after saturation. The measured longitudinal coherence time for the longer seeded columns

lengths of 3 and 4 mm are 0.8 ps and 1.0 ps respectively. These values are similar to the

measured pulse duration of 1.13 ± 0.47 ps for a seeded solid target Ne-like Ti laser [5], that

our model computations predict to be close to the pulse duration of the seeded Ni-like Mo

laser, 1.3-1.5 ps. In contrast, the measured temporal coherence time is much shorter than the

4-6 ps duration computed for the ASE Ni-like Mo laser, that in turn resembles the measured

~5ps pulse durations of other similar transient collisional grazing incidence ASE lasers that

were accurately predicted using the same model [18]. Therefore, it is concluded that while the

injection-seeded and ASE lasers are measured to have very similar linewidths, the seeded

laser has a significantly higher degree of temporal coherence that approaches full temporal

coherence. The coherent time of the injection-seeded Ni-like Mo laser is also several times

shorter than the transform limited pulsewidth of 4.7 ps reported for the 32.9 nm OFI laser [8],

corroborating the high potential of injection-seeded transient collisional solid target amplifiers

for the development of table-top SXRLs of shorter pulse duration.

Acknowledgments

This work was supported by the NSF Center for Extreme Ultraviolet Science and Technology

under NSF Award EEC-0310717, by the Chemical Sciences, Geosciences and Biosciences

Division, Office of Basic Energy Sciences, U.S. Department of Energy.


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